The standard kinematic relation for motion with constant acceleration is

$v^2 = u^2 + 2ax$

where:

• $v$ = velocity after displacement $x$
• $u$ = initial velocity
• $a$ = constant acceleration

Step 1: Relate the given graph to the equation

A graph of $v^2$ versus $x$ is a straight line of the form

$v^2 = (2a)x + u^2$

So, in the graph:

• slope $= 2a$
• y-intercept $= u^2$

Step 2: Use the graph information

From the given $v^2$ vs $x$ graph, the slope is $2$.

Therefore,

$2a = 2$

Step 3: Calculate acceleration

$a = 1\ \text{m/s}^2$

Final Answer

$\boxed{1}$